Final answer:
The correct option is a. The parallel component of a submarine's weight as it climbs at a 30° angle is given by mg sin(30°), which is represented by option (a). This is calculated using the sine of the incline angle multiplied by the full weight of the submarine.
Step-by-step explanation:
The component of the submarine's weight parallel to its motion as it climbs at an angle of 30° is given by mg sin(30°). The weight of the object acts directly downwards due to gravity, and when resolved into components on an incline, the parallel component is the product of the full weight (mg) and the sine of the angle of the incline (sin(θ)). In this case, the angle given is 30°.
When resolving forces on an inclined plane, it's important to draw a right triangle formed by the weight vectors. The angle of the incline is the same as the angle formed between the weight vector (w) and the component of the weight perpendicular to the slope (W₁). By using basic trigonometry, one can calculate the parallel and perpendicular components of the weight force:
- The parallel component (W‖) is w sin(θ) = mg sin(θ).
- The perpendicular component (W₁) is w cos(θ) = mg cos(θ).
Therefore, for a submarine climbing at a 30° angle, the parallel component of its weight is mg sin(30°), which corresponds to option (a).